Joomla 1.5

You can fix this if you disable WYSIWYG editor in Global Configuration. To do that, go to Site > Global Configuration and for Default WYSIWYG Editor select "Editor - No Editor". Then get back to edit your article (or Custom HTML module) and try to re-enter your code and save again. HTML won't be cut off now.

Joomla 1.6, 1.7 and later

To disable HTML filtering, go to Content > Article Manager > Options. Then select the Text Filters tab. My guess is you are editing site as Super User, so select "No Filtering" option in the Super Users row. Your HTML code will not be cut of after this (if you are editing site as Super User), no matter what WYSIWYG editor you are using.

Joomla 2.5

In this version of Joomla, text filtering options looks the same as on previous version, but they are now moved to the new place. You can access them in Site > Global Configuration > Text Filters.